Having just returned from a cruise with Royal Caribbean, I can tell you that they had a large board by the gangway and in large black letters they stated Alcohol, Beers and Wines were forbidden to be brought on board etc etc.

However I did not see any mention on that big notice about soft drinks / non-alcoholic beverages.

I saw some people bringing non-alcoholic beverages on board and they went through the security scanner without having their bottles confiscated.

I believe that security are only interested in stopping alcohol and will let soft drinks and water to be brought on board. The fact that their large notice does not mention non-alcoholic drinks seems to confirm that view.